There can be many answers to this question. If you are looking for a specific one that is out of a textbook or teacher instruction, consult your notes. "Raj" is a good term. The British referred to India as "the jewel in the crown," to describe how the British viewed the colony. I think that other terms can be used to describe it, depending on the point of view one assumes. For example, British politicians viewed the period of British rule in India as an excellent economic and political opportunity to continue their presence in South East Asia. For Indians, the period of British rule in India was seen as a complex element. On one hand, so much of India today was formed from British Rule. Recently, on a trip to Oxford, Prime Minister Manmohan Singh argued that the Indian judicial system, educational institution, and other elements relied heavily from their British counterparts. At the same time, many of the abuses in denial of freedom, both economic and political, could have led many Indians to argue that the period of British rule in India was known as a "living hell."

I believe that the term that you are looking for in this question is "Raj." The time when the British ruled India is typically known as the British Raj. The term comes from a couple of Indian languages and means something like "reign."

The British Raj is generally said to have begun in 1858 and to have ended in 1947. This is not the same time period in which the British were in control of India. There was a long period before 1858 when India was pretty much controlled by the British East India Company. After 1858, the British government ruled India as a colony. This is the period properly referred to as the Raj.